David W. answered • 10/29/15

Experienced Prof

First, re-read the problem until you understand it and can put it into your own words. How's this? There are three consecutive integers. Five times the second integer minus 57 equals the sum of the first and third integer. What's the third number?

Then, if possible, assign a variable to the value the problem wants you to find (so you won't forget to solve for it later). Here, let x = third integer.

Translate:

"first and third ... are added, the result is 57 less than five times the second integer"

means (x-2) + (x) = - 57 + 5 * ( x - 1 )

So, now the easy math:

(x-2) + (x) = -57 + 5(x-1) [rewrite equation]

2x - 2 = -57 + 5x - 5 [collect terms; distribute]

-3x = -60 [subtract 5x from each side]

x = 20 [divide each side by -3]

Checking:

Is 18 + 20 = -57 + 5*19 ?

38 = -57 + 95 ?

38 = 38 ? yes